Model Conditioned Data Elasticity in Path Analysis: Assessing the “Confoundability” of Model/Data Characteristics

Much research has been directed at the validity of fit indices in Path Analysis and Structural Equation Modeling (e.g., Browne, MacCallum, Kim, Andersen, & Glaser, 2002; Heene, Hilbert, Draxler, Ziegler, & Bühner, 2011; Hu & Bentler, 1999; Marsh, Hau, & Wen, 2004). Recent developments (e.g., Preacher, 2006; Roberts & Pashler, 2000, 2002) have encouraged researchers to investigate other criteria for comparing models, including model complexity. What has not been investigated is the inherent ability of a particular data set to be fitted with a constrained set of randomly generated linear models, which we call Model Conditioned Data Elasticity (DE). In this article we show how DE can be compared with the problem of equivalent models and a more general problem of the “confoundability” of data/model combinations (see MacCallum, Wegener, Uchino, & Fabrigar, 1993). Using the DE package in R, we show how DE can be assessed through automated computer searches. Finally, we discuss how DE fits within the controversy surrounding the use of fit statistics.